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arXiv:0907.5345 · The European Physical Journal D

Robust stationary entanglement of two coupled qubits in independent environments

M. Scala, Rosanna Migliore, A. Messina, L. L. Sánchez-Soto

Published Sep 10, 2010• 22 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2010-00230-5

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We investigate the entanglement dynamical behavior of two coupled qubits via a Heisenberg XX interaction, which are connected with two independent finite temperature heat baths. By numerical simulations of the quantum master equation, it is found that the interesting phenomena of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. We also show that two critical temperatures T 1 (determining that the quantum state is entangled or separable) and T 2 (where maximal stationary entanglement can be observed) exist, and stationary entanglement exhibits a non-monotonic behavior as a function of the finite temperature noise strength. These results enlarge the domain of the reasonable experimental temperature where stationary entanglement can be observable.
We analyze a one-dimensional ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super- and subradiant behavior. Moreover, each two-level system is coupled to another independent environment, modeled by a classical white noise, simulating a dephasing bath and described by the Haken-Strobl master equation. Single-exciton superradiance, an example of a cooperative quantum coherent effect, is destroyed at a critical dephasing strength proportional to the system size, showing robustness of cooperativity to the action of the dephasing environment. We also show that the coupling to a common decay channel contrasts with the action of dephasing, driving the entanglement decay to slow down on increasing the system size. Moreover, after a projective measurement which finds the excitation in the system, the entanglement reaches a stationary value, independent of the initial conditions.
In this paper, we review some results concerning the dissipative dynamics of two coupled qubits interacting with independent reservoirs. In particular, we focus on the role of counter-rotating terms in the qubit-qubit coupling, showing that their presence is the origin of stationary entanglement, which also turns out to be robust with respect to temperature. We also discuss the performances of different non-Markovian approaches in the description of the qubit-qubit dynamics, by considering a simplified exactly solvable Hamiltonian model.